Question

A merchant sold a product at 20% profit. Instead, had the merchant purchased the product for Rs 90 less and sold it at the same selling price, he would have made a profit of 40%
Find the cost price of the product​

Answer 1

Given:

A merchant sold a product at a 20% profit.

Instead, had the merchant purchased the product for Rs 90 less and sold it at the same selling price, he would have made a profit of 40%

To find:

The cost price of the product​

Solution:

Let "x" be the cost price of the product.

Profit% = 20%

∴ The S.P. of the product = $\frac{100 + 20}{100} \times x = \frac{120}{100}\times x = \frac{6x}{5}$

Now if the merchant purchased the product for Rs. 90 less

Then, New C.P. = (x - 90)

But the S.P. remains same i.e., → $\frac{6x}{5}$

∴ $New\:Profit = New\:S.P. - New\:C.P. = \frac{6x}{5} - (x - 90) = \frac{6x}{5} - x + 90$

Since the new gain% is given as 40%, so we can form an equation as:

$\frac{\frac{6x}{5} - x + 90}{(x - 90)} \times 100 = 40$

$\implies \frac{\frac{6x}{5} - x + 90}{(x - 90)} \times 5 = 2$

$\implies (\frac{6x}{5} - x + 90) \times 5 = 2\times (x - 90)$

$\implies 6x - 5x + 450 = 2x - 180$

$\implies x + 450 = 2x - 180$

$\implies 2x - x = 450 + 180$

$\implies \bold{x = 630}$

Thus, the cost price of the product is → Rs. 630.

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Answer 2

A merchant sold a product at 20% profit. Instead, had the merchant purchased the product for Rs 90 less and sold it at the same selling price, he would have made a profit of 40%